The Waste is a vast wasteland in the land of Ingary where no one dares to venture of their own free will. It is located in the south-western corner of the kingdom.
The Waste itself is a great expanse of barren, arid desert, seemingly of packed clay. Nothing grows here, and there is hardly ever any weather - only hot sun.
At the borders of the Waste lays a large garden. First started by Wizard Suliman and continued by Wizard Howl, it was created to try to fence in the Witch of the Waste. Sophie Hatter collects fresh flowers here daily for her flower shop when in hiding with Howl.
The Witch's Castle
The Witch of the Waste lived in a tall, spindly castle that appeared to be made of sandy clay flower pots stacked one-atop-another. Inside is much larger than it appears outside (in contrast to Howl's moving castle, which is only a small house within, but a large castle outside). However, it is also mostly empty.
In the Movie
In the movie, the Waste and the Folding Valley seem to be one in the same, or at least very closely related. The hilly grasslands around the valley and the surrounding mountains seem to be referred to as the Waste quite often in the movie, without any notion of an actual wasteland.
Approximately 50 years before the beginning of the novel, the Witch of the Waste, whose name is now seemingly unknown, was banished by the King of Ingary and his Royal Wizards to live out her days in exile in the Waste. Bitter and resentful, she was eventually able to make her way back into the kingdom proper with the death of the king who had exiled her.
The Waste is first seen when Sophie is lured there by the Witch of the Waste after recieving a message to rescue Lily Angorian. He travels there using Howl's Seven-League Boots. She arrives at the Witch's castle, where the Witch reveals that is was a trick to get Sophie to come to the Waste which had been successful. Howl flies Sophie across the Waste, revealing that Lily Angorian was the Witch's Fire Demon, which had consumed her and she was his true antagonist.
Howl's Moving Castle (film)
The Waste is first seen when the Castle is travelling through it. As mentioned above, the Waste in the film is different from the one in the books. Also, the garden at the edge of the Waste is shown to be merged with the Porthaven Marshes as Howl's Secret Garden.